If the distance from 3rd base to home plate is 60 feet, and the average speed of a pitch is 40mph, how many seconds would you have to get to home from 3rd before the ball reaches the catcher?

Answer: number is the number so we can be a number

Step-by-step explanation:

Answer:

56,513,230

Step-by-step explanation:

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The inverse of f(x) is f⁻¹(x) = (x - 3)/3.

To find the inverse of the function f(x), we need to switch the roles of x and y and solve for y.

Given:

f(x) = 3x + 3

Step 1: Replace f(x) with y:

y = 3x + 3

Step 2: Swap x and y:

x = 3y + 3

Step 3: Solve for y:

x - 3 = 3y

3y = x - 3

y = (x - 3)/3

Therefore, the inverse of f(x) is f⁻¹(x) = (x - 3)/3.

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The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

We have to given that;

To find correct variables which are continuous.

Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.

Hence, The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

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Answer:

Step-by-step explanation:

you have to find the mean of the two fractions, adding and then dividing by two

(1/5 + 1/9) : 2 =

14/45 : 2 =

7/45

Answer:

21cm

Step-by-step explanation:

Pythagoras Theorem for right angled triangle a² = b² + c²

hypotenuse² = opposite ² + adjacent ²

Call vertical height of wall (where ladder meets it) H

call ladder L and call ground distance G

50cm = 0.5m

3² = 0.5² + H², H² = 3² - 0.5² = 9 - 0.25 = 8.75. H = √8.75.

length of ladder is always 3m.

After ladder has slipped, G is now 0.5 + 0.7 = 1.2m.

H² = 3² - 1.2²

    = 9 - 1.44

    = 7.56

H = √7.56

H has changed from √8.75 to √7.56

It has slipped (√8.75 - √7.56)m

= 0.208m

= 20.8 cm

=21cm to nearest cm.

To have an infinite number of solutions the value of a would be

D. 20

Information given in the problem includes

5(x - 3) + a = 5(x + 1)

To have an infinite number of solutions we can simplify as follows

5(x - 3) + a = 5(x + 1)

opening the parenthesis

5x - 15 + a = 5x + 5

collecting like terms

-15 + a = 5

Adding 15 to both sides, we get:

a = 20

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Step-by-step explanation:

if the length of a Square Garden is 49 feet than what it is area

The inverse matrix used to decrypt the message is given as follows:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

To obtain the inverse matrix, we must have the original matrix side by side with the identity matrix, as follows:

[tex]\left[\begin{array}{cc}2&9\\1&5&\end{array}\right] \left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]

Then we must do row operations on the right matrix so we end with the identity matrix on the right and the inverse matrix on the right.

First we divide the first line by 2, hence:

[tex]\left[\begin{array}{cc}1&4.5\\1&5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\0&1&\end{array}\right][/tex]

Then we want the element a row 2 column 1 to be of zero, hence:

R2 -> R2 - R1

[tex]\left[\begin{array}{cc}1&4.5\\0&0.5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-0.5&1&\end{array}\right][/tex]

Then we want the diagonal element of the second row to be of 1, hence we multiply by 2, thus:

[tex]\left[\begin{array}{cc}1&4.5\\0&1&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-1&2&\end{array}\right][/tex]

Finally, we want the element of 4.5 to be of zero, hence:

R1 -> R1 - 4.5R2

Then:

[tex]\left[\begin{array}{cc}1&0\\0&1&\end{array}\right] \left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

The inverse matrix is of:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

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The points are shown on the number line as below.

The given numbers are,

-8/5 and 1.8

Now convert -8/5 into decimal form

therefore,

Divide 8 by 5 we get,

-8/5 = -1.6

Since we know that,

On a number line, arithmetic procedures can be better described. To begin, one needs understand how to locate numbers on a number line. A number line's midway point is zero.

Positive numbers occupy the right side of the zero on the number line, whereas negative numbers occupy the left side of the zero. The value of a number diminishes as we travel to the left side. 1 is greater than -2, for example.

Integers, fractions, and decimals may all be simply expressed on a number line.

The points are plotted on number line shown below.

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The description of the difference between the graph of g(x) and f(x), based on the equation relating the functions is the option C.

A function is a definition or rule that maps an input on to an output.

The possible function, obtained from a similar function on the internet can be presented as follows;

f(x) = 2ˣ

g(x) = 2·f(x) = 2·(2ˣ)

Therefore;

The graph of g(x) can be obtained from the graph of f(x), by a transformation of vertical stretch by factor of 2 and the correct option therefore is option C.

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[tex]\tan(44^o )=\cfrac{\stackrel{opposite}{29}}{\underset{adjacent}{x}} \implies x=\cfrac{29}{\tan(44^o)}\implies x\approx 30.03[/tex]

Make sure your calculator is in Degree mode.

Answer:

4√10

Step-by-step explanation:

distance = √((16-4)²+ (12-8)²)

= √(144 + 16)

=√160

=√(4X4X10)

=√4 X √4 X √10

= 2 X 2 X √10

= 4√10

Any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.

There are many other real-world situations where an equation of a line of fit can be useful in making predictions. For instance, a business owner could use data on sales and time to forecast future sales and plan inventory accordingly. A scientist could use data on temperature and precipitation to predict crop yields and plan agricultural strategies. An economist could use data on interest rates and inflation to forecast future economic trends and plan investment strategies. In general, any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.

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Two times a number c when subtracted from 6 times the number is equal to 4

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These arithmetic operations are;

From the information given, we have that;

6c - 2c = 4

The variables are c

The coefficient are 6 and 2

The constant is 4

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By rewriting the 3 given systems, we will see that:

1) Independent and inconsistent.

2) Independent and consistent.

3) Independent and inconsistent..

Let's analyze each system.

Let's look at the first one, we can rewrite it as:

y = 3x - 1

And, 2y - 6x = 4

2y = 6x + 4

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

Now let's look at the second system, we can rewrite it as:

2y = - x + 6

And, 4y + 2x = 12

y = - 1/2x + 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

For the final system we have:

y = 2x + 3

x + y = - 9

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

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To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.

Let's solve the first equation for x in terms of y:

x + 4y = -9

x = -4y - 9

Now we substitute this expression for x into the second equation:

2x + 5y = -6

2(-4y - 9) + 5y = -6

Simplifying this expression, we get:

-8y - 18 + 5y = -6

-3y = 12

y = -4

Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:

x + 4y = -9

x + 4(-4) = -9

x - 16 = -9

x = 7

Therefore, the solution to the system is x = 7, y = -4.

Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:

A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16

B) 21-4y-9)+5% -6 = -4y + 6

C) 2x+5(4-9)=-6 = 2x - 25 = -6

D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6

The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.

This acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.

In recent years, Sheffield Transportation has acquired three used buses for their transportation fleet. The decision to purchase these buses was likely made to meet the growing demand for transportation services in the area, while also keeping costs down by opting for used vehicles instead of new ones.

It is important to note that when purchasing used buses, Sheffield Transportation would have had to ensure that the vehicles were in good condition and met safety standards before putting them into service. Overall, this acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.

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The area of the object in the image shown in the attachment below is calculated as: 62 cm².

The area of the object can be found by decomposing the figure into two rectangles - larger rectangle and smaller rectangle.

Area of the larger rectangle = length * width

Length of the larger rectangle = 5 cm

Width of the larger rectangle = 4 cm

Area of the larger rectangle = 5 * 4 = 20 cm²

Area of the smaller rectangle = length * width

Length of the larger rectangle = 7 cm

Width of the larger rectangle = 6 cm

Area of the larger rectangle = 7 * 6 = 42 cm²

Area of the object = 20 + 42 = 62 cm².

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Answer:

To find the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7), we first need to find the center and radius of the circle.

The center of the circle is the midpoint of the diameter, which can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.

Using (4,-7) and (-12,-7) as the endpoint coordinates, we get:

Midpoint = ((4 + (-12))/2, (-7 + (-7))/2) = (-4, -7)

So the center of the circle is (-4, -7).

The radius of the circle is half the length of the diameter, which is:

Radius = 1/2 × distance between (4,-7) and (-12,-7)

Radius = 1/2 × (4 - (-12)) = 8

So the radius of the circle is 8.

Now we can write the equation of the circle in standard form:

(x - h)² + (y - k)² = r²

Where (h,k) is the center of the circle and r is the radius.

Substituting the values we found, we get:

(x - (-4))² + (y - (-7))² = 8²

Simplifying this equation, we get:

(x + 4)² + (y + 7)² = 64

Therefore, the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7) is (x + 4)² + (y + 7)² = 64.

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The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.

To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.

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The measure of length c using the law of cosines is 11.79 units

from the question, we have the following parameters that can be used in our computation:

The triangle (see attachment)

The measure of length c is calculated using the following law of cosines

c² = a² + b² - 2ab * cos(C)

So, we have

c² = 10² + 3² - 2 * 10 * 3 * cos(120)

Evaluate

c² = 139

Take the square root of both sides

This gives

c = 11.79

Hence, the value of c is 11.79

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cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.

Therefore, the exact value of cos 30° is (√3)/2.

Answer:

cos30 = √3 / 2

or cos30 ≈ 0.8660254037

Answer:

plus (+)

Step-by-step explanation:

Assume there is a number such as 1 after the minus:

[tex] - 1 + ( - 1) = - 2[/tex]

Thus - (+) - = +, since they add the minuses.

In the graph, differential is 4 or (p+k)-p = k as well as difference is -2 when y = 7 or y = 5, respectively.

A graph comprises a visual representation and diagram that displays facts or values in an organised manner in mathematics. The points of a graph are widely used to depict the connections between various objects. A. The difference between y = 7 or y = 5 is 4 and -2, respectively B. 4 is the difference, so (p+k)-p = k C. It differs by -2 D. Part C depends on 'k' rather than 'p,' not 'p'.

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